I understand the proof except for the following:(adsbygoogle = window.adsbygoogle || []).push({});

Suppose that -m_{2}< nx < m_{1}for positive integers m_{1}, m_{2}, n, and real number x.

Then there is an integer m with -m_{2}≤ m ≤ m_{1}such that m-1 ≤ nx < m.

It definitely sounds reasonable, but it seems like a big jump in logic.

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# Rudin Theorem 1.20 (b)

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